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3 years ago

In circle A shown below, Segment BD is a diameter and the measure of Arc CB is 48°:

Mathematics

2 answers:

marshall27 [118]3 years ago

8 0

Answer:

66°

Step-by-step explanation:

See attached picture.

When an angle intercepts an arc, ARC AC, and forms in the center [central angle], the angle has SAME measure as the ARC AC [denoted by x]. When the angle formed is on the opposite side, it has a measure HALF of that ARC AC [denoted $0.5x$ ]

If you look at the problem given, ∠DBC is intercepted by ARC DC and falls in the opposite side of the circle, NOT in the CENTER. Hence ∠DBC has a measure that is HALF of ARC DC.

There are 360 degrees in a circle. ARC DB has 2 endpoints that are the diameter of the circle, so ARC DB has a measure of 180 degrees. Also,

ARC DB = ARC DC + ARC CB

ARC DB = ARC DC + 48

180 = ARC DC + 48

ARC DC = 180 - 48 = 132

Since, ∠DBC = 0.5 * ARC DC, we have:

∠DBC = 0.5 * (132)

∠DBC = 66

Our answer is the second choice of 66°.

SCORPION-xisa [38]3 years ago

4 0

Hello,

Arc CD=180°-48°=132°

the measure of ∠DBC=132°/2 =66°

Answer B

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3 years ago

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3 years ago

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Answer:

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2 years ago

3q+4+9=-14 what is Q

BlackZzzverrR [31]

Hi! Your answer is q = -9

Please see an explanation for a better and clear understanding to your problem.

Any questions about my answer and explanation can be asked through comments! :)

Step-by-step explanation:

Since we want to solve for q-term. That means we are going to isolate q-term.

$\huge{3q+4+9=-14}$

We can add 4 and 9 together.

$\huge{3q+13=-14}$

Because we want to know the value of q. That means we have to isolate q-term by subtracting both sides by 13.

$\huge{3q+13-13=-14-13}\\\huge{3q=-27}$

We are reaching to the final step where we divide the whole equation by 3.

$\huge{\frac{3q}{3}=-\frac{27}{3}}\\\huge{q=-9}$

Finally, the solution for this equation is q = -9. But what if you are not certain or sure about the answer? Let's check it out!

To check the answer, simply substitute q = -9 in the equation.

$\huge{3q+4+9=-14}\\\huge{3(-9)+13=-14}\\\huge{-27+13=-14}\\\huge{-14=-14}$

Notice that the equation is true for q = -9. Hence, we can conclude that the solution for this equation is q = -9.

Hope this helps!

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3 years ago